2017 RI H2 Physics Prelims P3 QP

This document consists of 23 printed pages and 1 blank page. © Raffles Institution 9749/03 [Turn over Centre Number Index Number Name Class 3016 RAFFLES INSTITUTION 2017 Preliminary Examination PHYSICS Higher 2 Paper 3 Longer Structured Questions 9749/03 19 September 2017 2 hours Candidates answer on the Question Paper. No Additional Materials are required. READ THESE INSTRUCTIONS FIRST Write your index number, name and class in the spaces at the top of this page. Write in dark blue or black pen in the spaces provided in this booklet. You may use pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. The use of an approved scientific calculator is expected, where appropriate. Section A Answer all questions. Section B Answer one question only and circle the question number on the cover page. You are advised to spend one and half hours on Section A and half an hour on Section B. The number of marks is given in brackets [ ] at the end of each question or part question. For Examiner’s Use Section A 1 / 10 2 / 10 3 / 11 4 / 10 5 / 9 6 / 10 Section B (circle 1 question) 7 / 20 8 / 20 Deduction Total / 80

2 © Raffles Institution 9749/03 DATA AND FORMULAE Data speed of light in free space c = 3.00 × 108 m s−1 permeability of free space µ0 = 4 π × 10−7 H m−1 permittivity of free space ε0 = 8.85 × 10−12 F m−1 = (1/(36π)) × 10−9 F m−1 elementary charge e = 1.60 × 10−19 C the Planck constant h = 6.63 × 10−34 J s unified atomic mass constant u = 1.66 × 10−27 kg rest mass of electron me = 9.11 × 10−31 kg rest mass of proton mp = 1.67 × 10−27 kg molar gas constant R = 8.31 J K−1 mol−1 the Avogadro constant NA = 6.02 × 1023 mol−1 the Boltzmann constant k = 1.38 × 10−23 J K−1 gravitational constant G = 6.67 × 10−11 N m2 kg−2 acceleration of free fall g = 9.81 m s−2 Formulae uniformly accelerated motion work done on/by a gas W = p∆V hydrostatic pressure p = ρgh gravitational potential Gm rφ = − temperature T/K = T/°C + 273.15 pressure of an ideal gas 21 3 Nm Vpc= mean translational kinetic energy of an ideal gas molecule 3 2E kT= displacement of particle in s.h.m. 0 sinxx t ω= velocity of particle in s.h.m. v = v0 cos ω t 22 0xxω= ±− electric current I = Anvq resistors in series R = R1 + R2 + . . . . resistors in parallel 1/R = 1/R1 + 1/R2 + . . . . electric potential V = Q/(4πε0r) alternating current/voltage x = x0 sinωt magnetic flux density due to a long straight wire 0 2B d µ π= I magnetic flux density due to a flat circular coil 0 2 NB r µ= I magnetic flux density due to a long solenoid 0Bn µ= I radioactive decay x = x0 exp(−λt) decay constant 1 2 ln 2 tλ = 21 2s ut at= + 22 2v u as= +

3 © Raffles Institution 9749/03 [Turn over BLANK PAGE

4 © Raffles Institution 9749/03 Section A Answer all the questions from this section in the spaces provided. 1 A buoy floats in the sea next to a seawall. A lamp at the top of the buoy oscillates through a vertical distance of 0. 22 m, as shown in Fig. 1.1. The oscillations are simple harmonic with a frequency of 0.40 Hz. Fig. 1.1 (a) Define simple harmonic motion. [2] (b) State the amplitude of the oscillation. amplitude = m [1] (c) Calculate the angular frequency of the oscillation. angular frequency = rad s−1 [2] lamp 0.22 m seawall byoyy buoy sea

5 © Raffles Institution 9749/03 [Turn over (d) On Fig. 1.2, sketch the variation of the velocity of the lamp with its displacement from the equilibrium position as it moves downwards from its equilibrium position to its lowest position. Label the axes with appropriate values. Take upward displacement to be positive. Fig. 1.2 [2] (e) The lamp is above the top of the seawall for 1.8 s for each cycle of oscillation. Determine the distance of the equilibrium position of the lamp from the top of the seawall. distance = m [3] velocity / m s−1 displacement / m 0

6 © Raffles Institution 9749/03 2 Fig. 2.1 shows a dipper vibrating at a constant frequency on the surface of a pond. Ripples spread out as progressive transverse waves with circular wavefronts. Assume that the energy of the wave is spread over the entire circumference of the ripple and that no energy is lost in the propagation of the ripple. Two identical plastic balls placed on the water surface at points P and Q are observed to move up and down. The distance between points P and Q is shorter than one wavelength. Fig. 2.1 The variation of the displacements of points P and Q with time is shown in Fig. 2.2. The solid line represents point P and the dotted line point Q. Fig. 2.2 (a) Explain what is meant by a progressive transverse wave. progressive : transverse: [2] (b) State the period of the wave. period = s [1] P Q dipper top view ripple P Q 0 −1.0 −2.0 time / s 2.0 4.0 6.0 8.0 0.0 displacement / mm 2.0 1.0

7 © Raffles Institution 9749/03 [Turn over (c) Determine the phase difference between the waves reaching points P and Q. phase difference = rad [2] (d) The distance of point P from the dipper is 150 mm. Use Fig. 2.2 to show that the distance of point Q from the dipper is 600 mm. [2] (e) Using answers in (c) and (d), determine the wavelength of the ripples. wavelength = mm [2] (f) On Fig. 2.3, s ketch a possible variation of the displacement of a wave with distance from the dipper for two wavelengths. Numerical values are not expected. Fig. 2.3 [1] displacement distance 0

8 © Raffles Institution 9749/03 3 (a) A satellite orbits the Earth at a constant speed and height . Two radio waves transmitters on the surface of the Earth emit coherent waves of equal amplitudes, as shown in Fig. 3.1. Fig. 3.1 The intensity of the signal that the satellite receives varies periodically. (i) State what is meant by coherent waves. [1] (ii) Explain why the intensity of the signal varies periodically. [3] (iii) The transmitters are 150 m apart and the radio waves emitted have a wavelength of 1.2 m. The speed of the satellite is 8.0 × 103 m s−1 and the signal it receives varies in intensity with a frequency of 4.0 Hz. Calculate the height of the satellite above the surface of the Earth. height = m [3] satellite Earth transmitters orbit

9 © Raffles Institution 9749/03 [Turn over (b) The Arecibo telescope is one of the largest telescopes on Earth which scans the sky for sources that emit electromagnetic waves. The dish of the tel escope has a diameter of 300 m. Two distant sources are emitting radio waves of wavelength 1.2 m. They are separated by a distance of 2.0 × 1012 m from each other and 3.0 × 1016 m from the telescope. (i) Determine whether the telescope can resolve these two sources. [3] (ii) Fig. 3.2 shows the intensity distribution of the diffraction pattern formed by one of the sources. Sketch the intensity distribution of the other source if the diffraction patterns formed by the two sources are just resolved according to the Rayleigh criterion.